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JEE Physics Solved Question Paper 2010

Multiple Choice Questions

The quantities RC and $(\frac{L}{R})$ (where R, L and C stand for resistance, inductance and capacitance respectively) have the dimensions of

force
linear momentum
linear acceleration
time

The number of significant figures in 0.002305 is

A body travelling with uniform acceleration crosses two points A and B with velocities 20 ms^-1 and 30 ms^-1 respectively. The speed of the body at the mid-point of A and B is nearest to

25.5 ms^-1
25 ms^-1
24 ms^-1
$10 \sqrt{6} {ms}^{- 1}$

An aeroplane flies around a square field ABCD of each side 1000 km. Its speed along AB is 250 kmh^-1, along BC 500 kmh^-1, along CD 200 kmh^-1 and along DA 100 kmh^-1. Its average speed (in kmh^-1)over the entire trip is

225.5
175.5
190.5
310.5

Free fall of an object (in vacuum) is a case of motion with

uniform velocity
uniform acceleration
variable acceleration
constant momentum

6.
The maximum height of a projectile is half of its range on the- horizontal. If the velocity of projection is u, its range on the horizontal is

$\frac{2 u^{2}}{5 g}$

$\frac{3 u^{2}}{5 g}$

$\frac{4 u^{2}}{5 g}$

$\frac{u^{2}}{5 g}$

$\frac{4 u^{2}}{5 g}$

Maximum height = Range × $\frac{1}{2}$

$\frac{u^{2} \sin^{2} θ}{2 g} = \frac{u^{2} \sin 2 θ}{g} \times \frac{1}{2} \frac{\sin^{2} θ}{2} = \frac{2 \sin θ . \cos θ}{2} \tan θ = 2$

$∴ \sin θ = \frac{2}{\sqrt{5}} and \cos θ = \frac{1}{\sqrt{5}} ∴ R = \frac{2 u^{2} \sin θ . \cos θ}{g} = \frac{2 u^{2} \times \frac{2}{\sqrt{5}} \times \frac{1}{\sqrt{5}}}{g} R = \frac{4 u^{2}}{5 g}$

A stone of mass 2 kg is tied to a string of length 0.5 m. If the breaking tension of the string is 900 N, then the maximum angular velocity, the stone can have in uniform circular motion is

30 rad s^-1
20 rad s^-1
10 rad s^-1
25 rad s^-1

The position of a particle is given by $\vec{r} = 2 t^{2} \hat{i} + 3 t \hat{j} + 4 \hat{k}$ , where t is in second and the coefficients have proper units for $\vec{r}$ to be in metre. The $\vec{a} (t)$ of the particle at t = 1 s is

4 ms^-2 along y-direction
3 ms^-2 along x-direction
4 ms^-2 along x-direction
2 ms^-2 along z-direction

A passenger getting down from a moving bus, falls in the direction of the motion of the bus. This is an example for

moment of inertia
second law of motion
inertia of motion
inertia of rest

10.

A body of mass 6 kg is hanging from another body of mass 10 kg as shown in figure. This combination is being pulled up by a string with an acceleration of 2 ms^-2. The tension T₁ is, (g =10 ms^-2)